Malcolm Turnbull has confirmed he has been lobbying his former Liberal colleagues since being deposed as prime minister to refer Peter Dutton to the High Court over his eligibility to sit in parliament.

Section 44 of the constitution bans people from parliament who have “any direct or indirect pecuniary interest with the public service of the Commonwealth”.

Mr Turnbull, who has been in New York since quitting parliament, tweeted Thursday morning he has appealed to Prime Minister Scott Morrison and other Liberal MPs to force a definitive ruling on Mr Dutton’s political future.

“He [Mr Dutton] should be referred to the High Court, as Barnaby [Joyce] was, to clarify the matter,” he tweeted.

The point I have made to @ScottMorrisonMP and other colleagues is that given the uncertainty around Peter Dutton’s eligibility, acknowledged by the Solicitor General, he should be referred to the High Court, as Barnaby was, to clarify the matter.

In the absence of a referral from the government, Mr Turnbull has urged his Liberal former colleagues to cross the floor of the House and vote with Labor to force a referral of the Dutton case.

Mr Morrison said he welcomed – but won’t be distracted by – advice from his predecessor.

“I’ll obviously make the decisions in relation to our government on what I believe is in the national interest and based on the most recent and most timely information that I have available to me,” the Prime Minister told reporters Thursday.

“I think people have had enough of the lawyer’s picnics on these sort of issues and they want to focus completely and totally on what the nation needs here and now,” he said.

Mr Turnbull’s resignation after the leadership spill cost the government its one-seat majority. A by-election for his eastern Sydney seat of Wentworth will be held on October 20.

If Mr Dutton, who holds a slim margin in his seat of Dickson, was referred to the High Court, it would further weaken the Morrison government’s hold on power.

On the morning of the second leadership spill on August 27, Solicitor-General Stephen Donaghue released a statement saying there was “some risk” the High Court would find Mr Dutton has a conflict of interest over federal payments to his childcare centres.

But Mr Donaghue found it was unlikely Mr Dutton would be disqualified by reason of payments made to his family trust.

A supporter of Mr Dutton, anonymously speaking to Fairfax media, slammed Mr Turnbull’s manoeuvring as damaging to the government.

“Malcolm is hurting, I understand that,” the supporter was quoted as saying. “But this is desperate nonsense. He has no regard for the Prime Minister and no regard for the Liberal Party.”

Mr Morrison rejected calls from the Opposition in parliament on Monday that Mr Dutton be referred to the high court.

“The Australian people have had a gutful of these games. They want us to get on with business,” the Prime Minister said.